I agree with the others, the stone is worth the time and effort to pallet and resell / or use on a future project.
An excavator with thumb would be my preferred machine. Grab what you can from up top, pick a spot and excavate a ramp down, then finish moving debris from the bottom setting it up top.
Two dumpsters, a trash and a metal dumpster. You might not have enough metal to get paid for the scrap...but you probably will have enough to get it hauled away free. Have the dumpsters there and direct load as much as you can to keep from handling the debris twice.
After you get all of the debris out, put a pallet on forks (if you have them) and drive down in the hole with your tractor. Put the pallet up to the rock wall -close to the top, and start stacking rock.
Not sure how much weight you can lift, but you can do the math and figure how many pallets you will need for the rock. My guess even if you have a helper, this is going to take a few days.
Not sure of your plans for the excavator after the rock removal? If you planned on using it to backfill, the rock salvage operation will interfere and likely push you past your one week rental. If so, once you have cleaned up on the inside, you could use the excavator bucket to tip the rock into the hole, the use your bucket on the tractor to scoop and remove. Haul to the topside and dump.
This will make it harder to palletize, but you can always do a little at a time on your schedule.